The present invention relates to a method for determining the impedance characteristics of an interconnect or a series of transmission lines as represented by time domain reflectometry (TDR) characteristic waveforms, and more particularly to a method of enhancing the accuracy and resolution for such impedance determinations from TDR waveforms by providing greater immunity to noise.
Transmission lines propagate electromagnetic signals with a given ratio between electric and magnetic fields as defined according to the characteristic impedance of the transmission line. A discontinuity in a transmission line, where one impedance meets another impedance, creates a reflective boundary. An incident electromagnetic signal propagating within the transmission line when meeting the reflective boundary will have a portion of its energy reflected by the discontinuity, the percentage of the incident electromagnetic signal reflected being related to the magnitude of the impedance discontinuity.
With reference to FIG. 1, a TDR waveform 4 reveals the impedance discontinuities of a transmission line. An incident step signal 2 is applied in a forward direction to the input of the transmission line which corresponds to the leading transition 5 of the TDR waveform at time t=0. A partial reflection of the incident step returns, at a time subsequent the incident step signal. Transition 6 of the TDR waveform reveals the impedance discontinuity responsible for producing the partially reflected step. The time T.sub.rt at which the partially reflected step is received is equal to the round trip time required for the incident step to propagate to and from the discontinuity. The magnitude of the reflected signal with respect to the incident step is related to the magnitude of the impedance discontinuity. ##EQU1##
.GAMMA. is the reflection coefficient of the discontinuity. V.sub.refl is the magnitude of the partially reflected step and V.sub.in is the magnitude of the incident step. Z.sub.0 and Z.sub.1 are the preceding and subsequent characteristic impedances respectively for the transmission line segments defining the impedance discontinuity. A given time interval, time slice, along the time axis of the TDR waveform represents a given segment or layer of the transmission line.
Ideally, the incident step would have an infinite slope for its leading transition; however, real world sources cannot provide such abrupt transitions. Therefore, the incident step which is applied to the transmission line or device under test, DUT, has a finite rise time. With reference to FIG. 2, a DUT having a round trip propagation delay less than the rise time 10 of the associated incident unit step produces a "bump" 12 for the TDR waveform. The bump comprises a series of waveform segments 14, 16 and 17 which span a time interval representative of the round trip propagation delay between first and second impedance discontinuities, associated with the input and output respectively of the DUT, convolved with the leading transition of the incident step signal and multiple reflections thereof. Thus, the resolution for the TDR measurement is limited by the rise time of the incident step signal. In addition, the multiple discontinuities of the DUT make the relationship between the DUT and TDR waveform less intuitive and make it more difficult to extract the impedance levels associated with the DUT.
To obtain an impedance level for a DUT having a short dimension, the DUT s TDR waveform is analyzed in comparison with a reference TDR waveform. Referring to FIG. 2, the reference TDR waveform 13 is generated by applying the incident step signal upon a known discontinuity, e.g. a short, and recording the reference TDR waveform according to the signal produced by the known discontinuity in response to the incident step. After obtaining the reference TDR waveform, the known discontinuity is replaced with the DUT. The incident step signal is applied to the DUT and the signal as produced by the DUT in response to the incident step is measured for obtaining the DUT's TDR waveform 12.
With reference to the example of FIG. 2, the reference TDR waveform 13 has a 200 picosecond rise time associated with the leading transition 10 for the reflected step signal. The 200 picosecond rise time of the reference TDR waveform is much longer than the electrical delay corresponding to the physical length of the device under test, which is a 150 ohm, 25 picosecond long transmission line connected in series between two 50 ohm transmission lines. When the incident step is applied to the DUT, it produces the DUT s TDR waveform bump 12 along the 50 ohm characteristic impedance base line.
It is known to use a peeling algorithm for characterizing the DUT associated with the TDR waveform bump. The peeling algorithm "peels" the DUT layer-by-layer and calculates an impedance for each layer as it "slices" through respective time intervals of the reference TDR waveform and the DUT's TDR waveform, For each slice, the peeling algorithm determines respective amplitudes of the DUT and reference TDR waveforms associated with the given slice and then calculates an impedance for the respective given layer of the DUT according to the two amplitudes.
With reference to FIG. 3, in step 20, the peeling algorithm references the reference TDR waveform with respect to the DUT's TDR waveform and establishes a characteristic impedance level for the baseline of the TDR waveform. In step 22, a new time interval is sliced from the reference and DUT TDR waveforms for determining the impedance level of the next i.sup.th layer of the DUT. In step 24, the respective waveform amplitudes are determined for the respective segments of the reference and DUT waveforms within the current time slice and in step 26, an impedance is calculated for the current i.sup.th layer of the DUT according to the respective waveform amplitudes determined. In step 28, the DUT and reference TDR waveforms are processed according to the impedance level just calculated for the current, i.sup.th, layer of the DUT and new reference and DUT TDR waveforms are extracted in preparation for the next, i+1, layer of the DUT. The new TDR waveforms represent the incident and reflected signals relative to the interface between the i and i+1 layers of the DUT.
The algorithm used for processing the old waveforms and producing the new waveforms is a known, inverse scattering, modified deconvolution algorithm. A. M. Bruckstein and T. Kailpathy, "Inverse Scattering for Discrete Transmission-line Models", 51 AM Rev., 1987, hereby incorporated by reference, which incorporates further explanation of the peeling algorithms, defines such an inverse scattering, modified deconvolution algorithm. When processing slices of the DUT's TDR waveform associate with the characteristic baseline and assuming no noise is present on the reference and DUT TDR waveforms, the inverse scattering, modified deconvolution algorithm produces new TDR waveforms which are identical to the old TDR waveforms with mere time offsets, the time offsets being representative of the propagation delay associated with the given processed layer. However, new TDR waveforms result when the impedance level for the layer just processed differs from the impedance level of the layer immediately preceding, again ignoring the effects of noise.
In step 30, the peeling algorithm determines if the analysis thus far (i.e. accumulation of layers) is sufficient for specifying the length of the DUT. If the algorithm has not sliced through all layers of the DUT, then steps 22 through 30 are repeated until the algorithm has sliced through enough of the TDR waveforms for characterizing the DUT, whereupon the peeling algorithm terminates at step 31.
When noise is present on the DUT and reference TDR waveforms associated with a given layer of the DUT, the peeling algorithm produces an erroneous impedance determination for a given layer of the DUT associated with the noise. Furthermore, because the inverse scattering, modified deconvolution algorithm processes the TDR waveforms according to the impedance levels of preceding layers, the erroneous result of the given layer propagates through the remainder of the peeling algorithm and produces erroneous impedance results for layers of the DUT subsequent the given layer.
The noise present on each of the TDR waveforms comes primarily from two sources: real world instrumentation limitations (i.e., flicker noise, thermal noise, . . . ) and the accumulation of round off errors associated with the inverse scattering, modified deconvolution processing. The inverse scattering, modified deconvolution processing contributes noise to the modified reference and DUT TDR waveforms as the peeling algorithm progresses through the many layers of the DUT. Both noise sources limit the peeling algorithm's ability to accurately characterize the DUT and it is not uncommon to encounter noise magnitudes as large as 1% to 5% with respect to the amplitude of the reference incident step.
One method for reducing the effects of noise upon the peeling algorithm comprises clipping an initial portion of the leading edge of the reference step waveform so that the reference step starts abruptly at some percentage of the final value. FIG. 4 shows a reference unit step with 20% of the leading transition clipped. With 20% clipping, the unit step starts abruptly at a value (0.5) which is 20% of its final value (0.25). With respect to the peeling algorithm of FIG. 3, the clipping step would be inserted between steps 20 and 22 and before the junction associated with the loop feedback path. Although clipping improves the peeling algorithm's immunity to noise, the clipping compromises the peeling algorithm's ability to resolve abrupt impedance discontinuities.
FIG. 5a shows how noise affects the peeled results and FIG. 5b shows how clipping reduces the noise errors. FIG. 5c reveals how clipping, when applied to the processing of ideal waveforms without noise, compromises the results. When the clipping level is too large, it provides such an abrupt transition that it produces a slow exponential 41 instead of an instantaneous 43 convergence for the solution's impedance step, the time constant of the exponential being proportional to the clip value. Furthermore, it may be shown that the shortened transition of the reference step produces an error which propagates through subsequent layers of the DUT's solution to cause residual ringing 45a, 45b . . .
Thus, the peeling algorithm processes TDR waveforms for extracting impedance levels and modeling transmission lines having multiple reflections and/or dimensions shorter than the stimulus rise time. Noise corrupts the impedance solutions for given layers of the DUT and in turn propagates through the peeling algorithm and corrupts the impedance solutions of subsequent layers of the DUT. Clipping reduces the effects of this noise, but often requires a clipping value so large as to produce residual ringing and compromise the peeling algorithm's ability to resolve abrupt impedance discontinuities.
It is accordingly an object of the present invention to provide an improved TDR measurement technique for providing enhanced resolution and accuracy.
It is another object of the present invention to provide a TDR measurement technique which provides enhanced resolution and accuracy with improved immunity to noise.
It is another object of the present invention to provide a TDR measurement technique enabling the use of smaller clipping values within a peeling process of the measurement technique for assisting the above objectives and reducing residual ringing.